Question

Rút gọn biểu thức A = \(\sqrt{x}\left(\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{3-\sqrt{x}}\right)\) (x ≥ 0, x ≠ 9).

Answer 1

\(\begin{array}{l}A = \sqrt x \left( {\frac{1}{{\sqrt x  + 3}} - \frac{1}{{3 - \sqrt x }}} \right)\\ = \sqrt x .\left( {\frac{{\sqrt x  - 3}}{{x - 9}} - \frac{{3 + \sqrt x }}{{9 - x}}} \right)\\ = \sqrt x \left( {\frac{{\sqrt x  - 3 + 3 + \sqrt x }}{{x - 9}}} \right)\\ = \sqrt x .\frac{2\sqrt x}{x-9} \\ = \frac{2x}{x-9}\end{array}\)